We study the property of uniform discreteness within discrete orbits of nonuniform lattices
in
, acting
on
by
linear transformations. We provide quantitative consequences of previous results by
using Diophantine properties. We give a partial result toward a conjecture of Lelièvre
regarding the set of long cylinder holonomy vectors of the “golden L” translation surface:
for any
,
three points of this set can be found on a horizontal line within a distance of
of
each other.
Keywords
golden L, discrete orbit, holonomy vectors, nonuniform
lattices, convergents of the continued fraction, Samuel
Lelièvre conjecture
